Numerical solutions of the five-dimensional vacuum gravity equations have been constructed, describing the formation of an extreme rotating black hole in finite time. In one class, initial data contain a Schwarzschild black hole that reaches an extreme rotational state in finite time. In the second class, an extreme black hole forms from vacuum initial conditions devoid of an event horizon. These results provide the first example of a violation of the third law of black hole mechanics (the impossibility of reaching extremality in finite time) in pure gravity, without matter. This disproves the universality of the law and underscores its dependence on the specific dynamical model. The solutions obtained deepen our understanding of gravitational collapse and the constraints of cosmic censorship in higher dimensions.
The third law of black hole mechanics, proposed by Stephen Hawking, forbids a hole from spinning up to its limit in finite time — much like a whirlpool would need an eternity to reach absolute speed. Yet numerical simulations in five dimensions break this rule.
Simulations showed that a non-rotating hole can accelerate to its extreme all by itself. Moreover, such a vortex can spring directly from empty space — with no initial matter at all. It's as if a perfect whirlpool were to suddenly appear in a calm ocean, flouting the laws of hydrodynamics. The discovery shakes the analogy between gravity and heat: rules once thought unshakable lose their grip in higher-dimensional worlds.
🎯 The third law of [tag:black_hole]black hole[/tag] mechanics was born from thermodynamics: there, absolute zero temperature is unreachable in a finite number of steps. For [tag:black_hole]black holes[/tag], extremal rotation corresponds to zero temperature. Now it turns out this threshold can be reached without a long buildup.